Discharge Chapter USFS RM245

10. Measuring Discharge For computing area, the mid-section method (see fig. 56) uses the vertical line of each measurement as the centerline of a rectangular subsection; subsection boundaries fall halfway between the centerlines. Discharge in the triangles at the water’s edge, where the water is too shallow to allow a meter reading, are negligible in terms of total discharge. Multiply the mean velocity for each subsection by the area of the subsection to compute the discharge (Qn) for the subsection. Sum all subsection discharges to get the total discharge (Q) for the cross-section. The equations for this process are given in a step-wise procedure, later in this chapter. The field procedure is much like shooting elevations along the cross-section, except the current meter is used instead of the leveling rod. A two-person crew works best, one to operate the current meter and one to take notes (fig. 57). In high streams, or with loose and slippery substrates, wading may be difficult and strenuous. Concentrating on the current meter can make

Stream discharge (Q) is the volume of water passing a cross-section per unit of time and is generally expressed as cubic feet per second (cfs). Discharge is simply velocity times cross-sectional area (Q = VA). Cross-sectional area is determined by stretching a tape across the channel to measure distance at the crosssection locations where depth is measured with a calibrated rod. Area is depth times width in small increments across the channel. A current meter is used to measure velocity at the same location as each depth measurement. Use a current meter for the initial velocity measurement and subsequent measurements. Use the float method for repeated velocity measurements where time is limited. Although width and depth measurements are made during the cross-section survey, they are measured and recorded separately for calculating discharge. Figure 56 shows the velocity-area method for measuring discharge using the mid-section method of area determination.

UNDERSTANDING STREAM FLOW MEASUREMENT Water in a channel flows at different rates depending on its location, so the area of the cross-section is divided into subsections, with one or more measurements taken for each. At least 25-30 measurements are needed for most channels, with no more than 5% of the total discharge (Q) in each. Use more subsections for broad or structurally complex cross-sections.

Figure 56. Diagram of velocity-area method for measuring discharge using the mid-section method of area determination.

Figure 57. Measuring current velocity with a Price AA flow meter.

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surface is 22 feet across; 22 ∏ 25 = an interval of 0.88 feet, which can be rounded to 0.9). Use closer intervals for the deeper parts of the channel.

it hard to maintain balance. If the cross-section is dangerous at high water, use a safety line and a life vest if it seems prudent, or return at a lower flow. The Forest Service (and most government agencies) use English units for discharge records. A detailed reference for measuring current velocity is Chapter l of the National Handbook of Recommended Methods for Water Data Acquisition (U.S. Geological Survey 1977).

2. Start at the water’s edge and call out the distance first, then the depth, then the velocity. Stand downstream from the current meter in a position that least affects the velocity of the water passing the meter. Hold the rod in a vertical position with the meter directly into the flow. Stand approximately 1 to 3 inches downstream from the tape and at least 18 inches from the meter.

CURRENT METERS Meters commonly used to measure current velocity include: Marsh-McBirney, Price AA, and Pygmy.1 Some brands have rotating cups (like an anemometer on a weather station) while others have a pair of electronic contacts on a small head. Older models read out by clicking or buzzing into a headset. Newer models have digital read-out. Most current meters mount on a top-setting rod, which allows the current meter to be easily set to the correct depth. Top-setting rods are recommended for discharge measurement because they make the process simpler and quicker. Examine the meter before going into the field, read the instructions, do a spin test before each measurement, perhaps even test it in running water-use a nearby stream, irrigation ditch, or a garden hose aimed at the cups. Check the batteries and take spares. If you have more than one meter, compare results from the same point and calibrate as necessary. Calibrate your meters prior to the field season. Meter calibration services are available from the U.S. Geological Survey and universities.

3. To take a reading, the meter must be completely under water, facing into the current, and free of interference. The meter may be adjusted slightly up or downstream to avoid boulders, snags and other obstructions. The note taker will call out the calculated distance interval, which the meter operator may decide to change (e.g., taking readings at closer intervals in deep, high-velocity parts of the channel). Record the actual distance called out by the meter operator as the centerline for the subsection.

• Take one or two velocity measurements at each subsection.

• If depth (d) is less than 2.5 feet, measure velocity ( ) once for each subsection at 0.6 times the total depth (d) measured from the water surface (e.g., if d is 2 feet, measure at 1.2 feet from the water surface, or 0.8 feet above the bottom).

• If depth (d) is greater than 2.5 feet, measure velocity ( ) twice, at 0.2 and 0.8 times the total depth (e.g., if d is 3 feet, measure at 0.6 ft. and 2.4 ft. from the water surface). The average of these two readings (+) is the velocity for the subsection.

PROCEDURE FOR CURRENT VELOCITY MEASUREMENT 1. Stretch a tape between the endpoints of your channel cross-section. Divide the distance between the water’s edges by 25 (at least) to set the interval for metering (e.g., the water

4. Allow enough time for each reading — a minimum of 40 seconds for most meters. The operator calls out the distance, then the depth, and then the velocity. The note taker repeats it back as it is recorded, as a check. Readings from some meters (clicks) must be converted by the note taker, while others read out digitally in

1

The use of trade and company names is for the benefit of the reader; such use does not constitute an official endorsement or approval of any service or product by the U.S. Department of Agriculture to the exclusion of others that may be suitable.

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The following formula defines the basic method for calculating discharge:

feet-per-second. Figure 58 shows the field record of width, depth, and velocity measurements. 5. Calculate discharge in the field (specifics in next section). If any section has more than 5% of the total flow, subdivide that section and make more measurements.

where Q is the total discharge, a is the area of a rectangular subsection, the product of width (w) and depth (d) for that subsection, and is the mean velocity of the current in a subsection.

Computing Discharge When the velocity measurement is complete, calculate the total discharge (Q). Determining total discharge accurately is a complex issue, and a variety of methods and equations exist. The mid-section method is currently recommended by the U.S. Geological Survey. (At the risk of offending those with the proper math skills, the method is explained step-by-step.)

1. Using the mid-section method, compute the area (an ) of each subsection:

where b is distance along the tape from initial point. “Lost” discharge in the triangular areas at the edges is assumed negligible.

Figure 58. Field notes of discharge measurement.

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If you have any questions about this computation, draw a hypothetical cross-section, assign current velocities (from 0 to 5 feet per second) to each vertical, and work out a sample discharge before going to the field. Field crew members should understand this procedure and be able to compute sample discharges before field work begins.

2. Next, multiply the subsectional area (an) by the mean velocity ( n) for the subsection to get the subsection discharge (Qn). If only one velocity measurement was taken at 0.6 depth, it is the mean velocity ( n). If two measurements ( 1 and 2 ) were taken at 0.2 and 0.8 depth, compute the mean value as below: n

=

1

+

2

2

FLOAT METHOD FOR CURRENT VELOCITY

3. To compute the discharge for each subsection, use the equation: Qn = an

A float measurement is a good, simple way to estimate discharge provided velocity has been previously metered and cross-sectional area calculated. Even where observers are not highly skilled or do not have a current meter available, readings of gage height and float velocity can provide a valuable record of stream flow. Personnel at guard stations, hosted campgrounds, summer camps, and other sites can collect regular stream flow measurements. Equipment for float method measurement is simple: a measuring tape, a timer (a digital watch), and 5-10 floats. For floats, use orange peel, a water-soaked block of wood, or other natural material that sinks at least halfway into the water, is visible from shore, won’t be moved by wind, and is expendable and non-polluting (e.g., not ping-pong balls and plastic jugs).

n

where Qn = discharge for subsection n, an = area of subsection n, and n

= mean velocity for subsection n.

The calculation repeats this process for each subsection, as shown below: Q1=a1 1, Q2=a2 2, Q3=a3 3, Q4=a4 4, and so on. .. 4. The subsection products are then added to get total discharge (Q):

Float Method Procedure

Q1 = Q1 + Q2 +Q3 +Q4 +Q5 and so on...

1. Measure and mark two points, at least two to three channel widths apart, at the channel crosssection. If stationing stakes are still in place, one or two may be left in the ground to serve as markers.

Thus, total discharge (Q) equals the sum of all discharges ( a ) , as stated earlier in the basic equation: Q=

(a

2. Two observers are best. One tosses the float into the channel above the marker and calls out when it crosses the upstream point. Toss each float a different distance from the bank to get a rough average of velocities.

).

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section. (This coefficient can range from 0.8 to 0.95 depending on the roughness of the channel.)

3. The downstream observer starts the timer, sighting across the stream from the lower point. When the float passes it, stop the watch and record the time. Repeat the procedure 5 to 10 times. Average the values to get the mean surface velocity, and then multiply it by a velocity adjustment coefficient of 0.85 to calculate the mean velocity of the entire cross-

4. Using the previously measured cross-sectional area, multiply velocity times area to find discharge (Q = VA). Record it on a data sheet with date, time, etc.

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